Maximum - practice problems
Number of problems found: 84
- Base and longest side
The base of a right angled triangle is 10 centimetres and the longest side is 26 centimetres. What is the area of the triangle?
- Pass a test
The student has to pass a test that contains 10 questions. For each of them, he chooses one of 5 answers, with just one being correct. The student did not prepare for the test, so he chooses the answers at random. What are the probabilities that the stude
- Nursing school
The following table shows 1000 nursing school applicants classified according to scores made on a college entrance examination and the quality of the high school from which they graduated, as rated by a group of educators: @TB@ Quality of High Schools S
- Error rate
The exam has 6 questions. Students have an error rate of 20% and can have a maximum of 1 question wrong. What is the probability that they will succeed?
- A paint
A paint tin is a cylinder 12cm and height 22 cm. Leonardo, the painter, drops his stirring stick into the tin and it disappears. Work out the maximum length of the stick.
- A missile
A missile is fired with a speed of 100 fps in a direction 30° above the horizontal. Determine the maximum height to which it rises? Fps foot per second.
- A cheetah
A cheetah was separated from his brothers on a hunting mission. The brothers were at the watering hole 120 km away. The lost cheetah knew that he had to make it back before sundown which was 1.5 hours away. His brothers had planned to leave the waterin
- The volleyball ball
The volleyball ball can have a circumference after inflation of at least 650 max 750 mm. What volume of air can this ball hold, if its circumference is the average of the minimum and maximum inflation of the ball.
- Jewelry factory
In a jewelry factory, three assemblers make beaded necklaces. Marcus can make 22 necklaces per hour all day long. Anita can make 25 necklaces for her first three hour of the days and then slow down to 16 necklaces for the rest of the day. Yara can make 2
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. In order not to attract attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal?
- 5-number summary
Given the following 5-number summary: 11, 19, 24, 30, 48 which of the statistics cannot be determined?
Megapizza will be divided among 100 people. First gets 1%, 2nd 2% of the remainder, 3rd 3% of the remainder, etc. Last 100th 100% of the remainder. Which person got the biggest portion?
- Largest possible cone
It is necessary to make the largest possible cone from an iron rod in the shape of a prism with dimensions of 5.6 cm, 4.8 cm, 7.2 cm. a) Calculate its volume. b) Calculate the waste.
- Duo mix
In one kilogram of meat of two colors is 650 g of pork, the rest is chicken. One kilogram of pork is 40 CZK more expensive than a kilogram of chicken. How many CZK cost one kilogram of chicken meat so that the price of one kilogram of meat of two colors i
In the two dining rooms in the recreational building, there are equally arranged chairs around the tables. A maximum of 78 people can dine in the first dining room and 54 people in the second. How many chairs can be around one table?
- Summer camp
Some boys or girls signed up for the summer camp, which has a maximum capacity of 200 children. The main leader noticed that during the evening start, he could arrange the participants exactly in the twelve-step, sixteen-step, or eighteen-step, and no one
- Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
- The shooter
The shooter shoots at the target, assuming that the individual shots are independent of each other and the probability of hitting each of them is 0.2. The shooter fires until he hits the target for the first time, then stop firing. (a) What is the most li
During the hygienic inspection in 2000 mass caterers, deficiencies were found in 300 establishments. What is the probability that deficiencies in a maximum of 3 devices will be found during the inspection of 10 devices?
- Derivative problem
The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive and the product of one with the other power of the other is maximal.